Two hundred fence posts are to be placed into the ground in a straight line, 2m apart. The fence posts are stacked in a pile along this same line, 2m from the position of the first post to be put in. Maybell is going to put in the posts one at a time in order, and each post she puts in is farther away from the pile. Maybell can only carry one post at a time, and so she always walks back to the pile to get the next post. If Maybell starts at the pile, how many kilometers mush she walk to finish the job?

jonathanxu999
Feb 10, 2018

#1**0 **

1st post she walks 2m to put the post in, then 2m back to the pile = 4m

2nd post is at the pile = 0

3rd = 4

4th = 8

5th = 12

nth one = (n-2) *4

Total distance = 4 + \(\sum_{2}^{200}\)(n-2)*4 meters (this assumes she walks back to the pile location after the final post placement)

78,808 m = 78.808 km

IF she doesn't walk back to the pile it is 396 m LESS.

ElectricPavlov
Feb 10, 2018

edited by
Guest
Feb 10, 2018

#2**+1 **

Note that Maybell walks

4m total to put in the first post [ 2 out, 2 back ]

8m total to put in the second post [ 4 out, 4 back ]

12m total to put in the third post....etc. [ 6 out, 6 back ] ....etc.....

For the first 199 posts, we have

4 (1 + 2 + 3 + .....+ 199)

The sum of the first 199 positive integers can be expressed as

199 * 200 / 2 = 19900

And 4 times this is 79600 m

For the last post...she walks 2m * 200 = 400 m and doesn't need to return to the pile

So...the total distance walked is 79600m + 400m = 80000 m = 8 km

CPhill
Feb 10, 2018